Republican presidential frontrunner Donald Trump has courted another controversy, this time for not correcting a supporter who said President Obama is a Muslim, and asked when America can "get rid of" Muslims. The billionaire businessman later withdrew from a party event in South Carolina.

Trump canceled out of Friday's Heritage Action Presidential Forum, and his campaign sought to explain his absence by saying, "Mr. Trump has a significant business transaction that was expected to close Thursday. Due to the delay, he is unable to" attend the event. "He sends his regrets."

The forum took place the day after Trump's failure to correct a supporter.

"We have a problem in this country, its called Muslims. We know our current president is one. You know he's not even an American," an unidentified man, wearing a "Trump" T-shirt, said at a question-and-answer town hall event in Rochester, New Hampshire, Thursday night, according to Reuters.

"But anyway, we have training camps growing where they want to kill us," the supporter added. "That's my question. When can we get rid of them?"

Trump, without challenging the man's statement and premise, replied, saying, "We're going to be looking at a lot of different things. And you know a lot of people are saying that and a lot of people are saying that bad things are happening out there. We're going to be looking at that and plenty of other things."

Trump later sought to defend himself. "The media wants to make this issue about Obama," he said in a statement to The Washington Post. "The bigger issue is that Obama is waging war against Christians in this country. Their religious liberty is at stake."

His campaign manager Corey Lewandowski added, "Mr. Trump was asked about training camps. Mr. Trump answered the question and said, 'If there are any, we will fix it.' He said, 'I will look into it.' The question was specifically about training camps."

However, Trump received criticism from both Republicans and Democrats.

"If somebody at one of my town hall meetings said that, I would correct them and I would say, 'The president's a Christian and he was born in this country. Those two things are self-evident,'" New Jersey Governor and Republican presidential candidate Chris Christie said on NBC Friday. "And I think you have an obligation as a leader to do that."

Vermont Senator Bernie Sanders, who is also in the race for Democratic presidential nomination, tweeted: "Trump must apologize to the president and American people for continuing the lie that the president is not an American and not a Christian."

"GOP front-runner Donald Trump's racism knows no bounds," Debbie Wasserman Schultz, chair of the Democratic National Committee, said in a statement. "This is certainly horrendous, but unfortunately unsurprising given what we have seen already. The vile rhetoric coming from the GOP candidates is appalling."

"Is anybody really surprised that this happened at a Donald Trump rally?" asked White House spokesman Josh Earnest after condemning Trump's failure. "I don't think anybody who's been paying attention to Republican politics is at all surprised. The reason for that is that the people who hold these offensive views are part of Mr. Trump's base."